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Motivés par les développements récents dans le domaine des nanosciences, nous étudions les propriétés statistiques et thermodynamiques des systèmes mésoscopiques. En particulier, nous nous concentrons sur les résultats connus sous le nom de théorèmes de fluctuation. Ces relations donnent des prédictions sur le comportement de différents quantités dynamiques dans des situations loin de l'équilibre, tout en tenant compte des fluctuations de l'évolution temporelle. La première partie de notre étude est consacrée aux relations existants entre les fluctuations et la théorie de la réponse. Nous commençons par dériver une relation fonctionnelle pour les systèmes quantiques forcés dans le temps qui généralise l'égalité de Jarzynski et dont l'expansion en l'intensité du forçage permet de retrouver les résultats de la réponse linéaire. Nous poursuivons ensuite ces considérations en nous intéressant aux états stationnaires de non-équilibre. Ceci est réalisé dans le cadre des processus stochastiques, dans lequel nous dérivons une relation de fluctuation pour les courants de non-équilibre traversant le système. Cette relation lie explicitement les fluctuations aux forces thermodynamiques, ce qui nous permet de développer ses conséquences au niveau de la théorie de la réponse non-linéaire. De cette manière, nous obtenons de nouvelles relations liant fluctuations et coefficients de réponse dans le régime non-linéaire. Dans la deuxième partie de ce travail, nous développons une connexion récente liant l'irréversibilité au désordre dynamique. Nous présentons des résultats expérimentaux montrant que la production d'entropie s'exprime comme la différence de deux quantités mesurant la brisure de symétrie sous renversement du temps au niveau du désordre temporel. Nous étudions ensuite les conséquences de cette relation dans le contexte de l'énergétique du traitement de l'information. En particulier, nous présentons une généralisation du principe de Landauer pour l'effaçage d'information. De la même manière, nous relions la dissipation à la génération d'information par les entités biologiques.

Ion beam erosion of solid surfaces is known to produce a variety of surface morpholo- gies, such as pits, mounds or crests. Very often self-organized patterns composed of highly correlated arrays of dots or ripples at sub-micrometer and nanometer length scale could be obtained. Ion beam erosion patterning have demonstrated the poten- tial to tailor related surface properties for optoelectronic and spintronic applications, such as modulated photoemission induced by quantum con¯nement of nanodots and magnetic anisotropy induced by nanoripples. On the other hand, one considerable practical importance and e®ect of ion beam erosion is that of surface smoothing of nanometer features, during etching or ¯lm deposition coincident with energetic species. In my dissertation, systematic investigations of ripple formation and smooth- ing during low energy Ar+ ion erosion of sapphire surfaces using synchrotron grazing incidence small angle x-ray scattering and atomic force microscopy are performed. It is found in the pattern formation that the wavelength of ripples can be varied over a remarkably wide range by changing the ion incidence angle. The ion induced viscous °ow smoothing mechanism explains the general trends of the ripple wavelength at low temperature and incidence angles larger than 30±. The behavior at high temper- atures suggests relaxation by surface di®usion. However, strong smoothing is inferred from the observed ripple wavelength near normal incidence, which is not consistent with either surface di®usion or viscous °ow relaxation. Furthermore, a real-time x- ray scattering experiment is presented showing that ion smoothing of a pre-patterned surface near normal incidence is consistent with the e®ect of a collision-induced lat- eral current. Quantitative agreement is obtained using ion-collision simulations to compute the magnitude of the surface current. The results lead to predictions for the surface morphology phase diagram as a function of ion beam energy and incidence angle that substantially agree with experimental observations. The ion-induced lat- eral current smoothing model is applicable to many surfaces that become amorphous but maintain the stoichiometry of bulk materials during ion bombardment.

Recent short pulse (femtosecond) laser experiments have shown the existence of a so called superelastic precursor for short time periods after shock wave formation. The superelastic precursor is characterised as having amplitude far greater than the Hugoniot Elastic limit. This work reviews the current orthotropic thermoelastic plastic-damage model developed at Cranfield University, which includes the ability to model high velocity, shock wave forming impacts. The current model is unable to reproduce the superelastic precursor. Recent methods of looking at plasticity are reviewed and model improvements are suggested to enable the Cranfield model to reproduce superelastic precursor waves. The methods investigated are both dislocation based as it is determined that it is necessary to model deformation on the microscale in order to achieve reproduction of phenomena on the timescales of the early stages of shock wave formation and propagation. The methods investigated are the so-called self-organisation of dislocations and a mobile and immobile dislocation method proposed by Mayer. The plasticity part of the model proposed by Mayer is suggested for further investigation, including implementation into the DYNA 3D hydrocode which contains the current Cranfield model, to numerically asses the models capabilities. Similar, the self-organisation model is put forward for further numerical analysis. Further, calculation of the continuum Cauchy stress using purely atomistic variables is investigated in the form of the virial stress. It is determined that the virial stress calculation is unsuitable for modelling shock waves, however an alternative atomistic stress calculation which is more suited to shock waves is discussed. It is proposed that this stress calculation could be used to investigate the stresses contained within the thin shock front.

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